On the hyperchaotic complex Lü system

Abstract

The aim of this paper is to introduce the new hyperchaotic complex Lü system. This system has complex nonlinear behavior which is studied and investigated in this work. Numerically the range of parameter values of the system at which hyperchaotic attractors exist is calculated. This new system has a whole circle of equilibria and three isolated fixed points, while the real counterpart has only three isolated ones. The stability analysis of the trivial fixed point is studied. Its dynamics is more rich in the sense that our system exhibits both chaotic and hyperchaotic attractors, as well as periodic and quasi-periodic solutions and solutions that approach fixed points. The nonlinear control method based on Lyapunov function is used to synchronize the hyperchaotic attractors. The control of these attractors is studied. Different forms A part of the results of this manuscript has been accepted for publication in the of hyperchaotic complex Lü systems are constructed using the state feedback controller and complex periodic forcing.

Simplified method and synchronization for a class of complex chaotic systems

“…Such as fractional-order complex Lorenz system, 15 time-delay complex Lorenz system, 16 complex Chen system, 17 complex Lü systems, 18 hyperchaotic complex Lü system, 19 and so on. Such as fractional-order complex Lorenz system, 15 time-delay complex Lorenz system, 16 complex Chen system, 17 complex Lü systems, 18 hyperchaotic complex Lü system, 19 and so on.…”

A Novel S-Box Design Algorithm and Fuzzy-Pid Controller Design for a 5-D Burke–shaw System With Hidden Hyperchaos

“…As far as we know, there is very little known on the theories of hidden hyperchaotic attractors in high-dimensional autonomous systems [26], [27]. From 2012 to 2014, some 4D hyperchaotic systems without any equilibrium were proposed [28]- [30]. In particular, the remarkable findings are the modified Lorenz-Stenflo 106 system and the generalized hyperchaotic Rabinovich system that both have hidden hyperchaotic attractors around a unique stable equilibrium [31], [32].…”

Function projective synchronization of two four-scroll hyperchaotic systems with unknown parameters

“…It is believed that hyperchaotic systems with multiscroll attractors can clearly improve the security of communication schemes by generating more complex dynamics. However, most of the reported hyperchaotic systems can only generate two-scroll attractors [13][14][15]. As far as we know, only two 4D hyperchaotic systems found up to now can generate four-scroll attractors [16,17].…”